Skip to main content
SpringerLink
Log in

On the use ofR-estimators in analyzing repeated measures incomplete block clinical trials with baseline values as covariates

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

This article develops a rank based inference using a dispersion function for repeated measures incomplete block designs (IBD) with baseline values as covariates. Scores, Waldtype and drop in dispersion tests are developed for testing slope equals zero and equality of treatment effects. Multiple comparison procedures are also developed usingR-estimators which are obtained by minimizing a piece-wise linear dispersion function. A consistent estimator of a scale parameter, which appears in test statistic as a standardizing constant, is discussed. A data set from pharmaceutical research, which compares 12μg and 24μg formoterol (asthma drug) solution aerosol with a placebo treatment, is analyzed using the result of this article.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adichie, J. N. (1978). Rank tests of sub-hypotheses in the general linear regression,Annals of Statistics, 6, 1012–1026.

    MATH  MathSciNet  Google Scholar 

  2. Arnold, S. F. (1981).The Theory of Linear Models and Multivariate Analysis. John Wiley and Sons Inc., New York.

    MATH  Google Scholar 

  3. Bloch, D. A. andGastwirth J. S. (1968). On a simple estimate of the reciprocal of the density function.Annals of Mathematical Statistics, 39, 1083–1085.

    MathSciNet  Google Scholar 

  4. Hettmansperger, T. P. (1984).Statistical Inference Based on Ranks. John Wiley and Sons, New York. Chapter 5.

    MATH  Google Scholar 

  5. Jaeckel, L. A. (1972). Estimating regression co-efficients by minimizing the dispersion of residuals.Annals of Mathematical Statistics, 43, 1449–1459.

    MathSciNet  Google Scholar 

  6. Jones, B., andKenward, M. G. (1987). The analysis of data from 2×2 cross-over trials with baseline measurements.Statistics in Medicine, 6, 911–926.

    Google Scholar 

  7. Jureckova, J. (1971). Nonparametric estimate of regression coefficients.Annals of Mathematical Statistics, 42, 1328–1338.

    MathSciNet  Google Scholar 

  8. Liang, K.-Y. andZeger, S. L. (1986). Longitudinal data analysis using generalized linear models.Biometrika, 73, 13–22.

    Article  MATH  MathSciNet  Google Scholar 

  9. McKean, J. W. andHettmansperger, T. P. (1976). Tests of hypotheses based on ranks in the general linear model.Communications in Statistics-Theory and Methods, A5(8), 693–709.

    MathSciNet  Google Scholar 

  10. Mehta, C. R. andPatel N. R. (1995). Exact logistic regression: Theory and examples.Statistics and Medicine, 14, 2143.

    Google Scholar 

  11. Mehta, C. R., Patel, N. R., Senchaudhury, P. andTsiatis, A. (1994). Exact permutation tests for group sequential trials.Biometrics, 50, 1042–1053.

    Article  MATH  Google Scholar 

  12. Nelder, J. A., andMead, R. (1965). A simple method for function minimization.The Computer Journal, 7, 308–313.

    Google Scholar 

  13. Patel, H. I. (1983). Use of baseline measurements in the two-period cross-over design.Communications in Statistics—Theory and Methods, 2693–2712.

  14. Rashid, M. M. (1995). Analysis of repeated measures incomplete block designs usingR-estimates.Statistics and Probability Letters, 22, 213–221.

    Article  MATH  MathSciNet  Google Scholar 

  15. Rashid, M. M., andNandram, B. (1995). A rank based analysis of one-way repeated measures designs with a changing covariate.Journal of Statistical Planning and Inference, 46, 249–263.

    Article  MATH  MathSciNet  Google Scholar 

  16. Rashid, M. M. (1994). A rank based approach to using baseline values in repeated measures incomplete block designs. Technical Report, Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609.

    Google Scholar 

  17. Rashid, M. M. andBagchi, A. (1997). Robust analysis of one-way repeated measures designs with multiple replications per cell.Statistica Sinica, 7, 647–667.

    MATH  Google Scholar 

  18. Senn, S. J. (1989). The use of baseline in clinical trials of brochodilators.Statistics in Medicine, 8, 1339–1350.

    Google Scholar 

  19. Senn, S. andAuclair, P. (1990). The graphical representation of clinica trials with particular reference to measurements overtime.Statistics in Medicine, 9, 1287–1302.

    Google Scholar 

  20. Schafer, W. D. (1981). Letters to the Editor.The American Statistican, 35, 179.

    Google Scholar 

  21. Senn, S. J. (1993).Cross-Over Trials in Clinical Research. John Wiley and Sons, Chichester, England, U.K.

    Google Scholar 

  22. Zeger, S. L. andLiang, K. Y., andAlbert, P. S. (1988). Models for longitudinal data: A generalized estimating equations approach.Biometrics, 44, 1049–1060.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Biometrics III, HFD 720, Center for Drug Evaluation and Research, Food and Drug Administration, 5600 Fishers Lane, 20857, Rockville, MD, U.S.A.

    M. Mushfiqur Rashid

Authors
  1. M. Mushfiqur Rashid
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Part of this work was completed when the author was a faculty member at Worcester Polytechnic Institute. Worcester, Massachusetts. The view expressed in this article are those of the author and not those of the United States. Food and Drug Administration.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rashid, M.M. On the use ofR-estimators in analyzing repeated measures incomplete block clinical trials with baseline values as covariates. J. It. Statist. Soc. 5, 261–284 (1996). https://doi.org/10.1007/BF02589176

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02589176

Keywords

Search

Navigation